2009 AMC 10 B, Problem #4—2009 AMC 12 B, Problem #4—“Each triangle has leg length12·(25-15) = 5meters.”SolutionAnswer (C):Each triangle has leg length12·(25-15) = 5meters andarea12·52=252square meters. Thus the flower beds have a total area of25 square meters. The entire yard has length 25 and width 5, so its areais 125. The fraction of the yard occupied by the flower beds is25125=15.Difficulty:Medium-easyNCTM Standard:Geometry Standard: analyze properties and determine attributes of two- andthree-dimensional objects.Mathworld.com Classification:Geometry>Plane Geometry>Miscellaneous Plane Geometry>Area
Twenty percent less than 60 is one-third more thanwhat number?Difficulty:MediumNCTM Standard:Algebra Standard: understand the meaning of equivalent forms of expressions,equations, inequalities, and relations.Mathworld.com Classification:Number Theory>Arithmetic>Fractions>Fraction
Kiana has two older twin brothers.The product oftheir three ages is 128. What is the sum of their threeages?(A)10(B)12(C)16(D)18(E)242009 AMC 10 B, Problem #6—2009 AMC 12 B, Problem #5—“Note that128 = 27.”SolutionAnswer (D):The age of each person is a factor of128 = 27. So the twinscould be20= 1,21= 2,22= 4,23= 8years of age and, consequently,Kiana could be12812= 128,12822= 32,12842= 8, or12882= 2years old,respectively. Because Kiana is younger than her brothers, she must be 2years old. The sum of their ages is2 + 8 + 8 = 18.Difficulty:Medium-easyNCTM Standard:Algebra Standard: identify essential quantitative relationships in a situationand determine the class or classes of functions that might model the relationships.Mathworld.com Classification: NEED CATEGORY!
By inserting parentheses, it is possible to give theexpression2×3 + 4×5several values.How many different values can beobtained?(A)2(B)3(C)4(D)5(E)62009 AMC 10 B, Problem #7—2009 AMC 12 B, Problem #6—“The three operations can be performed in any of3! = 6orders.”Difficulty:MediumNCTM Standard:Number and Operations Standard:understand meanings of operations andhow they relate to one another.Mathworld.com Classification: NEED CATEGORY! Which recreational math was it?
In a certain year the price of gasoline rose by 20%during January, fell by 20% during February, rose by25% during March, and fell byx% during April. Theprice of gasoline at the end of April was the same as ithad been at the beginning of January. To the nearestinteger, what isx?2009 AMC 10 B, Problem #8